39.11  More than one office prohibited.
  Statewide elected officials and members of the general assembly shall not hold more than one elective office at a time. All other elected officials shall not hold more than one elective office at the same level of government at a time. This section does not apply to the following offices:  county agricultural extension council or soil and water conservation district commission.
93 Acts, ch 143, §4; 2001 Acts, ch 158, §5

See also §441.17(1)